Diffuse Cloud Models: Successes and Challenges

We present the general physical conditions thought to be present in diffuse interstellar clouds. The radiation field is driving the atomic to molecular transition and the resulting physical conditions. We focus on the recent observational signatures of significant values of the cosmic ionization rate (10^-16 - 10^-15 s^-1) which should also impact the clues to Diffuse interstellar Bands.